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 Bihar Board 12th Maths Objective Important Questions Part 4

Bihar Board 12th Maths Objective Important Questions Part 4

Question 1.
The order of the differential equation 2x2d2ydx2+3dydx+y=0 is ’
(a) 3
(b) 2
(c) 1
(d) not defined
Answer:
(a) 3

Question 2.
The number of arbitrary constants in the general solution of a differential equation of fourth order are.
(a) 0
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Question 3.
The number of arbitrary constants in the particular solution of a differential equation of third order are :
(a) 3
(b) 2
(c) 1
(d) 0
Answer:
(d) 0

Question 4.
Which of the following differential equations hasy = c1ex + c2e-x as the general solution?
(a) d2ydx2 + y = 0
(b) d2ydx2 – y = 0
(c) d2ydx2 + 1 = 0
(d) d2ydx2 – 1 = 0
Answer:
(b) d2ydx2 – y = 0

Question 5.
Which of the following differential equations has y =x as one crits particular solution ?

Answer:
(c)

Question 6.
The general solution of the differential equation dydx = ex+y is ;
(a) ex + e-xy = c
(b) ex + ey = c
(c) e-x + ey = c
(d) e-x + e-y = c
Answer:
(a) ex + e-xy = c

Question 7.
A homogeneous differential equation of the front dxdy=h(xy) can be solved by marking the substitution : .
(a) y = Vx
(b) V = yx
(c) x = Vy
(d) x = V
Answer:
(c) x = Vy

Question 8.
Which of the following is a homogeneous differential equation :
(a) (4x + 6y + 5) dy – |3y + 2x + 4| dx = 0
(b) (xy) dx – (x3 + y3) dy = 0
(c) (x3 + 2y2)dx + 2xydy = 0
(d) y2dx + (x2 – xy – y3)dy = 0
Answer:
(d) y2dx + (x2 – xy – y3)dy = 0

Question 9.
The integrating factor of the differential equation xdydx−y=2x2 is :
(a) e-x
(b) e-y
(c) 1/x
(d) x
Answer:
(c) 1/x

Question 10.
The general solution of a differential equation of the type dxdy+P1x=Q1 is :

Answer:
(c)

Question 11.
The integrating factor of the differential equation
(a-y2)dxdy

Answer:
(d) 11−y2√

Question 12.
In triangle ABC, which of the following is not true :


Answer:
(c)

Question 13.
If a⃗  and b⃗  are two colliner vectors, then which of the following are incorrect:
(a) b⃗  = λ a⃗ , for some scalar λ
(b) a⃗  = ±b⃗ 
(c) The respective compounds of a⃗  and b⃗  are proportional
(d) Both the vectors a⃗  and b⃗  have some direction, but different magnitudes.
Answer:
(d) Both the vectors a⃗  and b⃗  have some direction, but different magnitudes.

Question 14.
Let the vectors a⃗  and b⃗  be such that |a⃗ | = 3 and |a⃗ |= 2√3, then a→×b→ is a unit vector, If the angle between a⃗  and b⃗  is :
(a) π6
(b) π4
(c) π3
(d) π2
Answer:
(b) π4

Question 15.
Area of a rectangle having vertics A, B, C and D with position :
Vectors −i^+12j^+4k^,i^+12j^+4k^,i^−12j^+4k^ and −i^−12j^+4k^ respectively is:
(a) 12
(b) 1
(c) 2
(d) 4
Answer:
(c) 2

Question 16.
If a⃗  is a nonzero vector of magnitude ‘a’ and λ nonzero scalar, then λa⃗  is unit vector If,
(a) λ = 1
(b) λ = -1
(c) a = |λ|
(d) a = 1|λ|
Answer:
(d) a = 1|λ|

Question 17.
The general solution of the differential equation
exdy + (yex +2x)dx = 0 is :
(a) xex + x2 = c
(b) xey + y2 = c
(c) yex + x2 = c
(d) yey + x2 = c
Answer:
(c) yex + x2 = c

Question 18.
If θ is the angle between two vectors a⃗  and b⃗ , the b⃗ , a⃗ , b⃗  ≥ 0 only when :
(a) 0 < θ < π2
(b) 0 ≤ θ ≤ π2
(c) 0 < θ < π
(d) 0 ≤ θ ≤ π
Answer:
(b) 0 ≤ θ ≤ π2

Question 19.
Let a⃗  and b⃗  be two unit vectors and θ is the angle between them; Then a⃗  + b⃗  is a unit vector if:
(a) θ = π4
(b) θ = π3
(c) θ = π2
(d) θ = 2π3
Answer:
(d) θ = 2π3

Question 20.
The value of i^(j^×k^)+j^(i^+k^)+k^(i^+j^) is :
(a) 0
(b) -1
(c) 1
(d) 3
Answer:
(c) 1

Question 21.
If θ is the angle between any two vectors a⃗  and b⃗  the |a⃗ ⋅b⃗ |a⃗ ⋅b⃗ |=|a⃗ ×b⃗ ∣ when θ, is equal to
(a) 0
(b) π4
(c) π2
(d) π
Answer:
(b) π4

Question 22.
The planes 2x – y + 4z = 5 and Sx – 2.5y + 10z = 6 are :
(a) perpendicular
(b) parallel
(c) intersect y-axis
(d) passes through (0, 0, 54
Answer:
(b) parallel

Question 23.
Distance between the two planes 2x + 3 y +-4z = 4 and 4x + 6y + 8x = 12 is
(a) 2 units
(b) 4 units
(c) 8 units
(d) 9 units
Answer:
(d) 9 units

Question 24.
The solution set of the in equation 2x + y > 5 is :
(a) half plane that contains the origin
(b) open half plane not containing the origin
(c) when xy-plane except the reints lying on the live 2x + y = 5
(d) none of these
Answer:
(b) open half plane not containing the origin

Question 25.
Which of the following is not a convex set ?
(a) {(x, y)/2x + 5y < 7}
(b) {(x,y)/x2 + y2 ≤ 4} .
(c) {x/ |x| = 5}
(d) {(x,y)/3x2 + 2y ≤ b
Answer:
(c) {x/ |x| = 5}

Question 26.
The reints of which the maximum value of x + y. Subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95,x,y ≥ 0 is obtained is :
(a) (30,25)
(b) (20,35)
(c) (35,20)
(d) (40,15)
Answer:
(d) (40,15)

Question 27.
Objective function of a LPP is :
(a) a constraint
(b) a function to be optimized
(c) a relation b/w the variables
(d) none of these
Answer:
(b) a function to be optimized

Question 28.
The Probability of obtaining an even prime number on each die, when a pair of dice is rolled is :
(a) 0
(b) 13
(c) 112
(d) 136
Answer:
(d) 136

Question 29.
If P (A) = 12 P(B) = 0 then P(A/B) is :
(a) 0
(b) 12
(c) not defined
(d) 1
Answer:
(c) not defined

Question 30.
If Aand B are two events such that P(A) ≠ 0 and P(B/A) = then :
(a ) A⊂B
(b ) B⊂A
(c) B = Φ
(d) A = Φ
Answer”
(a ) A⊂B

Question 31.
If P(B/A)>P(A) then which of the following is correct:
(a) P(B / A) < P(B)
(b) P(AnB)<P(A) P(B) (c) P(B/ A) > P(B)
(d) P(B/A) = P(B)
Answer:
(c) P(B/ A) > P(B)

Question 32.
Two events A and B will be independent, if:
(a) A and B are mutually exclusive
(b) P(A’B’)=[1-P(A)][1-P(B)]
(c )P(A) = P(B)
(d) P(A) + P(B) = 1
Answer:
(b) P(A’B’)=[1-P(A)][1-P(B)]

Question 33.
If A and B are any two events such that P(A) + P(B) – P (A and B) = P(A), the ;
(a) P(B/A) = 1
(b) P(A/B) = 1
(c) P(B/A) = 0
(d) P(A/B) = 0
Answer:
(b) P(A/B) = 1

Question 34.
Suppose that two cards are drown at random from a deck of cards. Let X be the number of aces obtained. Then the. value of E(X) is :
(a) 37221
(b) 913
(c) 113
(d) 213
Answer:
(d) 213

Question 35.
In a box containing 100 bulbs. 10 are defective. The probability that out of a sample of 5 bulbs, none in defective is :
(a) 10-1
(b) (12)5
(c) (910)5
(d) 910
Answer:
(c) (910)5

Question 36.
The probability that a student Is not a swimmer is 15 then the probability that mat of five students four are swimmers is:
(a) 5C4(45)415
(b) (45)415
(c) 5C115(45)4
(d) None of these
Answer:
(a) 5C4(45)415

Question 37.
The mean of the numbers of obtained on throwing a die having written. I on three facems, 2 on two faces and 5 on one face is :
(a) 1
(b) 2
(c) 5
(d) 83
Answer:
(b) 2

Question 38.
If y = log x then d2ydx2 =
(a) log x
(b) 1x
(c) −1x2
(d) 1x2
Answer:
(c) −1x2

Question 39.
ddx[ddx(sinx)]=
(a) sin x
(b) cos x
(c) -sin x
(d) -cos x
Answer:
(c) -sin x

Question 40.
∫ba[ddx(logx)]=
(a) log ba
(b) log ab
(c) log(a-b)
(d) log(b-a)
Answer:
(b) log ab

Question 41.
dy – dx = y – x hindi
(a) y + x = k
(b) y – x = k
(c) y/x = k
(d) xy = k
Answer:
(b) y – x = k

Question 42.
|2i⃗ +3j⃗ +5k⃗ |
(a) 10
(b) 10−−√
(c) 38
(d) 38−−√
Answer:
(d) 0

Question 43.
(5i⃗ +2j⃗ −k⃗ )⋅(i⃗ −2j⃗ −k⃗ )=
(a) 13
(b) 8
(c) 6
(d) 0
Answer:
(d) 0

Question 44.
ddx [(sin-1x + cos-1x)] =
(a) π2
(b) 0
(c) π22
(d) 1
Answer:
(b) 0